ERCIM News No.44 - January 2001 [contents]

A Graphical System for Internal Density Modelling by Coons Bodies

by Silvester Czanner and Roman Durikovic

The rise of solid modelling as a principal medium for mechanical product description can be traced to the requirement of informational completeness of geometric representations. Unfortunately, traditional geometry-based systems do not contain the important information neededfor some engineering designs. Many unambiguous solid representation techniques like primitive instancing, cell decomposition, constructive solid geometry have one limitation, they cannot offer ways of representing internal behavior.

In the mechanical industry it is very important to know not only the description of the surface, but also about the interior and the density of the object. Therefore, there was a need for a system which makes it possible to model the interior density of the 3D parameter solids.

A Project between the Software Department of the University of Aizu and the Department of Computer Graphics and Image processing of the Comenius University exists to support and develop a new methodology for representing an internal structure of density of 3D objects. The main goal of the project is to develop a graphical system for modelling and visualizing the interior structures and density of 3D objects. It allows a developer to make modifications into internal structure of 3D object in a natural and intuitive way.

The system can also modify and composite 3D objects (basic elements) to an arbitrary 3D shape. The elements used are so called parametric solids. We are using three types of parametric solids, namely Coons body 0, 1 and 2. The bodies are defined as an extension into four-dimensional space of well-known Coons patches in B-splines form.

Each of the three Coons bodies have different abilities to control the interior structure. The simplest and most limited is Coons body 0 where only the shape of quadrilateral can be changed. Coons body 1 allows the user to control the interior by modification the control points along the edge curves of a parametric solid. The most general is the Coons body 2, having the ability to modify shape and interior by all control points within the boundary surfaces of a parametric solid.

To understand the interior structure of 3D objects several visualization methods are used. The easiest way to visualize a parametric solid is to display it as a set of isoparametric surfaces. Another option is to visualize a shaded object together with projected parametric curves corresponding to constants u, v and w. The most difficult option is to show the interior changes in time as metamorphoses between two Coons bodies.

The most useful elements are Coons bodies 2. Since, any of them is a B-spline volume, the shape continuity is simply controlled in a similar way as it is for B-splines. The system can create more complicated shapes such as a composition of several Coons body elements.

Implementation is done under the Linux Red Hat 6.2 operating system and the objects are stored in a scientific format SILO.

The authors see the advantage of this graphical system in the ability to define the boundary and internal initial conditions prior to numerical simulations. Parametric solids can be effectively applied on finite elements with irregular or trimmed boundaries to avoid difficult problems in model design for Fine Elements Methods.

Please contact:
Silvester Czanner - SRCIM / Comenius University Bratislava

Roman Durikovic - University of Aizu, Japan